How to properly sharpen concave angle without affecting topology?
It seems you are using modifiers: Solidify and Subsurf.

The problem here, is that you don't have any real edge to apply crease.

First you should apply the Solidify Modifier, then you could get the edge in the red circle you drawn.

The crease amount will influence the shape, from completly smooth to completly sharp.

Alternatively, you could select the edge and apply a Bevel.

Select the edge, W, Bevel



Set the amount and the other properties in the panel (T)